Friday the 13th

Answer

Never. If we count backwards from Friday the 13th, we can find that Friday the 13ths only and always appear on months that have Sunday as the first. We can also assume, that out of 12 months, there is a 1.7 (12 months/7 days of the week) chance of there being a Sunday as the first day of the month. Since this number is over 100%, we can promise that there will never be a year without at least one Friday the 13th. Now isn't that unlucky!Hide

When a non-leap year starts on a Monday the first day of each month (Jan-Dec) fall on
Mon,Thurs,, Thurs, Sun, Tues, Fri,
Sun, Wed, Sat, Mon, Thur, Sat

In a leap year starting on a Monday the 1st day of the months fall on
Mon, Thur, Thur, Mon, Wed, Sat
Mon, Thur, Sun, Tues, Fri, Sun

In both cases there is a least 1 month starting on each day of the week. So, if the starting day of the year is shifted there will still be at least one month starting on a Sunday meaning there will be at least one Friday the 13th in any year.

There are only 14 possible distinctive calendars. One for each day Jan. 1 can start on for a non-leap year (7), and another set for leap year (7). If you look at each of these 14 possibilities, there is ALWAYS a year that has at least 1 month that will start on Sunday (resulting in Friday the 13th). Therefore, there will ALWAYS be a Friday the 13th in every year. It has nothing to do with probability.